How this calculator works
A discount security, such as a Treasury bill or a commercial paper note, pays no coupon. You buy it below face value and receive the face value at maturity. The holding period return is the gain divided by the purchase price. Bond equivalent yield annualises that return by multiplying by 365 divided by the number of days held, matching the 365-day basis used for many money-market quotations. It assumes the security is held to maturity and that the calendar-year length is 365 days. The result is a simple annualisation, not an effective annual rate.
Formula
Discount = face value - purchase price. Holding period return = discount / purchase price. Bond equivalent yield = (discount / purchase price) x (365 / days to maturity).
Worked example
A 180-day bill bought for $9,750 and redeemed at $10,000 has a discount of $250. The holding period return is 250 / 9,750 = 2.5641%, and the bond equivalent yield is 2.5641% x 365 / 180 = 5.1995%.
Advertisement
Frequently asked questions
How is this different from bank discount yield?
Bank discount yield divides the discount by the face value, which understates the return. Bond equivalent yield divides by the price you actually paid, so it reflects the money invested.
Why use 365 days rather than 360?
Different markets quote on different bases. Many Treasury and money-market calculations use 365 for bond equivalent yield, while some bank discount conventions use 360. This page uses 365 throughout.
Can the purchase price exceed face value?
Yes, but then the result is a negative yield, which is unusual for a discount security. The calculator reports the negative figure rather than hiding it.
Is bond equivalent yield the same as effective annual yield?
No. It is a simple annualisation. Compounding within the year would give a slightly higher effective annual rate for a security held less than a year.